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Talk:Ordinal Array Notation
Use this page to discuss this new notation and what we can do with it. JTOnstead20 (talk) 00:57, October 26, 2016 (UTC) When defining lists or tables of rules, try to keep entries of a same type on the same side, for example 0=w phi(n,0)=n just has poor form secondly, a paradox case in rule 2, n=0, makes phi(0,0)=1, and thus 0=1=0 =w from rule 1 you can "hack" that by labeling it as an exception, as was done to fix the NAN problem, but such hacks will diminish your googologist experience gain in the long run And lastly a problem in rule 3, from this rule forward the notation is stuck at phi(1,0,0) and no longer grows: 1(0) = phi(w,0) 2(0) = phi(phi.....(w,0),...0) = phi(1,0,0) 3(0) = phi(phi(1,0,0),0) = phi(1,0,0) phi(1,0,0) is a fixed point y such that phi(y,0)= y (Chronolegends (talk) 04:00, October 26, 2016 (UTC)). No OAN number is well defined byeond 1,1,1, as rule 4 references two unspecified notations "base Q" and "extended phi notation" (definition or link to them?) Q was originally created as a direct replacement for Weiermann's Theta Function where the omega was the Q. I'll replace the rules for that, then. As for extended phi notation, see the article for the small Veblen ordinal. It shows phi(1,0), phi(1,0,0), ... Extended phi is the act of having more than two numbers inside that parenthesis. Normal phi is (x,0) while extended phi is phi(x,0,0), phi(x,0,0,0), and so on. JTOnstead20 (talk) 19:38, November 3, 2016 (UTC) Right, but don't the definitions here in the talk page. the hole must be patched in the actual OAN Chronolegends (talk) 20:04, November 3, 2016 (UTC) Okay it is done. Thank you! JTOnstead20 (talk) 00:09, November 4, 2016 (UTC) What relationship do OAN and the Church-Kleene ordinal have? Is that ordinal the limit of OAN? JTOnstead20 (talk) 15:09, November 4, 2016 (UTC) A problem UUhhhmmmm..........there is a contradiction.You say the number of zeros is the second number and you even gave the example of \(\varphi(1,0,0,0) = 1,3\) and at the same time you say that the Feferman ordinal (\(\Gamma_0\)) is \(1,1\) even though in extended Veblen hierarchy \(\Gamma_0\) is \(\varphi(1,0,0)\) and should be \(1,2\) then.Also should I assume that if \(\varphi(\alpha,0) = 1+\alpha\) and that has one zero then \(\alpha\) should be short for \(\alpha,1\)?Oh and in that case,the real \(1,1 = 1 = \omega\).Boboris02 (talk) 20:21, February 18, 2017 (UTC) Limit of power So, we have the sequence: *1 = ε0 *1,1 = Γ0 *1,1,1 = ψ(ΩΩω) *1,1,1,1 = ψ(Ωω) *1,1,1,1,1 = ψ(ψI(0)) or ψ(α), where α is the first fixed point of α ↦ Ωα. etc. Each member of this sequence is denoted 1^n, where n is the number of "1"s. Looking at the original article, I see this is extended to: 1^1^1 = [1^1^1] = 1^ε0, so this is capable of handling transfinite numbers of arguments, as it should. Then it goes on to define 1^^α, 1^^^α, 1^^^^α, etc., presumably up to transfinite 1{β}α. My question, then, is: how strong is this notation at its limits? How strong is, say, 1^ω? 1^^ω? 1{ω}ω? Is it even well-defined that far in? If so, can we call 1{Ω}ω and turn this into an OCF, or better yet, further extend this through BEAF operators, such as Or am I just going mad? [[User:ArtismScrub|ArtismScrub] (talk) 17:45, January 18, 2018 (UTC)